Properties of Nonlinear Transformations of Fractionally Integrated Processes
UCSD Economics Discussion Paper No. 2000-07
25 Pages Posted: 1 Dec 2000 Last revised: 7 Aug 2009
Date Written: June 5, 2001
This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0). For non-stationary I(d) processes, every integer power transformation is non-stationary and exhibits a deterministic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.
Keywords: Nonlinear Transformations, Long Memory, Fractional Integration, Antipersistence, Nonstationarity, Hermite Rank, Moments
JEL Classification: C22
Suggested Citation: Suggested Citation